New Measurements of the European Muon Collaboration
Effect in Very Light Nuclei
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Seely, J. et al. “New Measurements of the European Muon
Collaboration Effect in Very Light Nuclei.” Physical Review
Letters 103.20 (2009): 202301. © 2009 The American Physical
Society
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http://dx.doi.org/10.1103/PhysRevLett.103.202301
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American Physical Society
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Thu May 26 06:26:42 EDT 2016
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PRL 103, 202301 (2009)
PHYSICAL REVIEW LETTERS
week ending
13 NOVEMBER 2009
New Measurements of the European Muon Collaboration Effect in Very Light Nuclei
J. Seely,1 A. Daniel,2 D. Gaskell,3 J. Arrington,4,* N. Fomin,5 P. Solvignon,4 R. Asaturyan,6,† F. Benmokhtar,7 W. Boeglin,8
B. Boillat,9 P. Bosted,3 A. Bruell,3 M. H. S. Bukhari,2 M. E. Christy,10 B. Clasie,1 S. Connell,5,‡ M. M. Dalton,5 D. Day,5
J. Dunne,11 D. Dutta,11,12 L. El Fassi,4 R. Ent,3 H. Fenker,3 B. W. Filippone,13 H. Gao,1,12 C. Hill,5 R. J. Holt,4 T. Horn,7,3
E. Hungerford,2 M. K. Jones,3 J. Jourdan,9 N. Kalantarians,2 C. E. Keppel,10 D. Kiselev,9 M. Kotulla,9 C. Lee,14
A. F. Lung,3 S. Malace,10 D. G. Meekins,3 T. Mertens,9 H. Mkrtchyan,6 T. Navasardyan,6 G. Niculescu,15 I. Niculescu,15
H. Nomura,16 Y. Okayasu,2,16 A. K. Opper,17 C. Perdrisat,18 D. H. Potterveld,4 V. Punjabi,19 X. Qian,12 P. E. Reimer,4
J. Roche,3 V. M. Rodriguez,2 O. Rondon,5 E. Schulte,4 E. Segbefia,10 K. Slifer,5 G. R. Smith,3 V. Tadevosyan,6 S. Tajima,5
L. Tang,10 G. Testa,9 R. Trojer,9 V. Tvaskis,10 W. F. Vulcan,3 F. R. Wesselmann,5 S. A. Wood,3 J. Wright,5
L. Yuan,10 and X. Zheng4
1
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
2
University of Houston, Houston, Texas, USA
3
Thomas Jefferson National Laboratory, Newport News, Virginia, USA
4
Physics Division, Argonne National Laboratory, Argonne, Illinois, USA
5
University of Virginia, Charlottesville, Virginia, USA
6
Yerevan Physics Institute, Yerevan, Armenia
7
University of Maryland, College Park, Maryland, USA
8
Florida International University, Miami, Florida, USA
9
Basel University, Basel, Switzerland
10
Hampton University, Hampton, Virginia, USA
11
Mississippi State University, Jackson, Mississippi, USA
12
Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina, USA
13
Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California, USA
14
University of the Witwatersrand, Johannesburg, South Africa
15
James Madison University, Harrisonburg, Virginia, USA
16
Tohoku University, Sendai, Japan
17
Ohio University, Athens, Ohio, USA
18
College of William and Mary, Williamsburg, Virginia, USA
19
Norfolk State University, Norfolk, Virginia, USA
(Received 28 April 2009; revised manuscript received 27 July 2009; published 13 November 2009)
New Jefferson Lab data are presented on the nuclear dependence of the inclusive cross section from 2 H,
and 12 C for 0:3 < x < 0:9, Q2 3–6 GeV2 . These data represent the first measurement of
the EMC effect for 3 He at large x and a significant improvement for 4 He. The data do not support previous
A-dependent or density-dependent fits to the EMC effect and suggest that the nuclear dependence of the
quark distributions may depend on the local nuclear environment.
3 He, 4 He, 9 Be
DOI: 10.1103/PhysRevLett.103.202301
PACS numbers: 13.60.Hb, 24.85.+p, 25.30.Fj
High energy lepton scattering provides a clean method
of probing the quark momentum distributions in nucleons
and nuclei. The early expectation was that probes at the
GeV energy scale would be insensitive to nuclear binding
effects, which are typically on the order of several MeV.
The effects were expected to be small except at large
Björken-x, corresponding to very high momentum quarks.
In this region, the rapid falloff of the parton distributions
approaching the kinematical limit of x ! 1 makes the
distributions very sensitive to the smearing effect of the
nucleon’s motion.
In 1983 the European Muon Collaboration (EMC) discovered that the per-nucleon deep inelastic structure function, F2 ðxÞ, in iron was significantly different than that for
deuterium [1]. They showed a clear suppression of high
momentum quarks for 0:3 < x < 0:8, confirmed for several
0031-9007=09=103(20)=202301(5)
nuclei in more extensive measurements at SLAC [2]. This
phenomenon, dubbed the ‘‘EMC effect,’’ has become the
subject of a determined theoretical effort aimed at understanding the underlying physics. While progress has been
made in explaining the principal features of the effect, no
single model has been able to explain the effect over all x
and A [3,4]. Much of the effort has focused on heavy
nuclei, and many models are evaluated for infinite nuclear
matter and scaled to the density of finite nuclei, neglecting
possible surface effects or the impact of detailed nuclear
structure.
There has been less focus on few-body nuclei, which
provide the opportunity to test models in cases where the
details of the nuclear structure are well understood. These
data are also necessary to get a complete picture of the
evolution of nuclei from deuterium to infinite nuclear
202301-1
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PRL 103, 202301 (2009)
PHYSICAL REVIEW LETTERS
matter. Precise measurements in few-body nuclei allow for
stringent tests of calculations of the effects of Fermi motion and nuclear binding, which is the dominant effect at
large x. In addition, these data allow us to test simple
scaling models of the EMC effect. A global analysis of
the SLAC data [2] found that the data could be equally well
described by fits that assumed the EMC effect to be proportional to the average nuclear density, , or by fits that
assumed it scaled with the nuclear mass, i.e., an EMC
effect proportional to lnðAÞ. These simple fits for the
nuclear dependence did equally well for heavy nuclei (A *
12), where the density varies slowly with A. For very light
nuclei, these simple models predict different behavior, but
the limited data on light nuclei were not sufficient to
differentiate between these predictions.
To address these issues, Jefferson Lab (JLab) experiment
E03-103 was proposed to make high precision measurements of the EMC effect at large x in both heavy and fewbody nuclei. The experiment ran in Hall C during the fall of
2004. The measurement used a 5.767 GeV, 80 A unpolarized electron beam, with scattered electrons detected in
the High Momentum Spectrometer (HMS). The primary
measurements were taken at a scattering angle of 40 , with
additional data taken at different angles and/or 5 GeV
beam energy to examine the Q2 dependence. Data were
collected on four cryotargets—1 H, 2 H, 3 He, and 4 He, and
solid Beryllium, Carbon, Copper, and Gold targets arranged together on a common target ladder. The target
ladder held only two cryotargets at a time, so there were
two separate running periods to collect data on all four
cryogenic targets. Data were taken on solid targets during
both periods for systematic checks on the relative normalization during the two run periods. In this Letter, we focus
on the light nuclei, A 12, for which fewer data exist and
which require smaller corrections due to backgrounds and
Coulomb distortion.
The HMS subtends a solid angle of 7 msr and the
momentum bite was restricted to the central part of the
acceptance (9%). The detector package consisted of two
sets of wire chambers for tracking, four planes of hodoscopes for triggering, and a gas Čerenkov and lead-glass
calorimeter for online and offline particle identification [5].
The cross sections were corrected for electronic and computer dead times, detector efficiencies, and radiative effects
(which closely followed the approach of Ref. [6]). Data
were taken at several beam currents on carbon to look for
rate-dependent corrections, and on all four cryotargets to
measure current-dependent target density effects due to
heating at high current.
The dominant sources of background were pion production, electrons scattering from the aluminum cryocell wall
and electrons from pair-production in the target. After
applying calorimeter and Čerenkov cuts, the pion contamination was negligible for the kinematics shown here. The
electron background (8%–19%) from the cell wall was
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subtracted using measurements on a ‘‘dummy’’ target,
consisting of two aluminum targets at the positions of the
cryocell walls, with radiative corrections calculated separately for the real cryocells and the dummy target. The
background from pair production was measured by reversing the HMS polarity to detect positrons, yielding a direct
measure of the charge-symmetric background, strongly
dominated by pair production. This background was typically 5%–10%, but was as much as 30% of the total yield at
the lowest x and largest Q2 values.
There are several sources of systematic uncertainty
which we separate into point-to-point and normalization
uncertainties. Normalization uncertainties are those that
modify the overall scale, but not the x or Q2 dependence
of the target cross section ratios, e.g., target thicknesses.
Point-to-point uncertainties can vary with x or Q2 , and are
treated in the same way as statistical uncertainties.
The cryogenic target thicknesses were determined from
the dimensions of the cryocell and the density of the
cryogen, as computed from measurements of its pressure
and temperature. The total normalization uncertainty in the
cross section ratios was between 1.6% and 1.9%, mainly
due to the 1%–1.5% uncertainty in the target thicknesses.
Uncertainty in the target boiling correction contributes
0:4%, radiative corrections [6] contribute 0.1%–0.75%,
depending on the kinematics and target thickness, and the
acceptance contributes 0.5% (0.2%) to the solid target
(cryotarget) ratios. The dominant sources of point-to-point
uncertainties come from charge measurement drifts
(0.3%), corrections due to drift of beam position on target
(0.45%), radiative corrections (0.5%), dead time determination (0.3%), detector efficiencies (0.3%), and acceptance
(0.3%). Charge-symmetric background subtraction contributes 0.1%–0.6% to the uncertainty, and is largest for
the Be and C targets. The uncertainties in the kinematics
contribute up to 0.6% to the uncertainties in the ratios, with
larger effects at large x values where the cross section is
changing most rapidly. We apply Coulomb distortion corrections following the effective momentum approximation
of Aste [7]. The corrections are &1% for 12 C, and much
smaller for the helium data.
The results are shown as ratios of the cross section per
nucleon, rather than the F2 structure functions. These
ratios are identical if the ratio of longitudinal to transverse
cross sections, R ¼ L =T , is independent of A. If RA RD , then there will be a correction involved in going from
cross section ratios to the F2 ratios [3].
In the Björken limit, the structure function exhibits
scaling, i.e., becomes independent of Q2 except for the
weak Q2 dependence from QCD evolution of the parton
distributions. This scaling has been observed in the deepinelastic scattering region, which for e-p scattering is
typically taken to be Q2 > 1 GeV2 and W 2 > 4 GeV2 ,
where W is the invariant mass of the unmeasured system.
In nuclei, it has been observed that results are nearly
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PRL 103, 202301 (2009)
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PHYSICAL REVIEW LETTERS
EMC ratio for 4 He is comparable to 12 C, suggesting that
the modification is dependent on the average nuclear density, which is similar for 4 He and 12 C, rather than a function
of nuclear mass.
Figure 3 shows the EMC ratio for 3 He, with the low-x
data from HERMES. Note that the HERMES 3 He data
have been renormalized by a factor of 1.009 based on
comparisons of their 14 N EMC effect and the New Muon
Collaboration 12 C result [10]. We show both the measured
cross section ratio (squares) and the ‘‘isoscalar’’ ratio
(circles), where the 3 He result is corrected for the proton
excess. Previous high-x EMC measurements used a correction based on an extraction of the F2n =F2p ratio for free
nucleons from high Q2 measurements of F2d =F2p . We use
global fits [11,12] to the free proton and neutron cross
sections evaluated at the kinematics of our measurement
and then broadened using the convolution procedure of
1.2
E03103 Norm. (1.6%)
σC/σD
1.1
SLAC Norm. (1.2%)
1
0.9
1.2
E03103 Norm. (1.7%)
1.1
σBe/σD
independent of Q2 to lower values of W 2 for Q2 * 3 GeV2
[8]. A precise measurement of the target ratios in the
resonance region [9] for Q2 ¼ 3–4 GeV2 showed that the
nuclear dependence is identical to the high Q2 measurements up to x 0:8, even though the deep-inelastic scattering region is limited to x < 0:5 for these Q2 values.
Because these data are at somewhat lower Q2 than
previous high-x results, typically Q2 ¼ 5 or 10 GeV2 for
SLAC E139 [2], extensive measurements were made to
verify that our result is independent of Q2 . The structure
functions were extracted at several Q2 values and found to
be consistent with scaling violations expected from QCD
down to Q2 3 GeV2 for W 2 1:5 GeV2 , while the
structure functions ratios show no Q2 dependence.
Figure 1 shows the carbon to deuteron ratio for the five
highest Q2 settings (the lowest and middle Q2 values were
measured with a 5 GeV beam energy). There is no systematic Q2 dependence in the EMC ratios, even at the largest
x values, consistent with the observation of previous measurements [3].
For all further results, we show the ratios obtained from
the 40 data (filled squares in Fig. 1). While there are data
at 50 (open circles) for all nuclei, the statistical precision
is noticeably worse, and there are much larger corrections
for charge-symmetric background and Coulomb distortion
(for heavier nuclei).
The EMC ratios for 12 C, 9 Be, and 4 He are shown in
Fig. 2 along with results from previous SLAC extractions.
The 4 He and 12 C results are in good agreement with the
SLAC results, with much better precision for 4 He in the
new results. While the agreement for 9 Be does not appear
to be as good, the two data sets are in excellent agreement
if we use the same isoscalar correction as E139 (see below)
and take into account the normalization uncertainties in the
two data sets. In all cases, the new data extend to higher x,
although at lower W 2 values than the SLAC ratios. The
SLAC Norm. (1.2%)
1
0.9
1.2
1.2
E03103 Norm. (1.5%)
2
Q =4.06
2
Q =4.50
1.1
σC/σD
1.1
σ4He/σD
Q2=4.83
2
Q =5.33
Q2=6.05
SLAC Norm. (2.4%)
1
1
0.9
0.2
0.9
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
FIG. 1 (color online). Carbon EMC ratios [17] for the five
highest Q2 settings (Q2 quoted at x ¼ 0:75). Uncertainties are
the combined statistical and point-to-point systematic. The solid
curve is the SLAC fit [2] to the Carbon EMC ratio.
FIG. 2 (color online). EMC ratios for 12 C, 9 Be, and 4 He [17],
compared to SLAC [2]. The 9 Be results include a correction for
the neutron excess (see text). Closed (open) circles denote W 2
above (below) 2 GeV2 . The solid curve is the A-dependent fit to
the SLAC data, while the dashed curve is the fit to 12 C.
Normalization uncertainties are shown in parentheses for both
measurements.
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PHYSICAL REVIEW LETTERS
1.2
E03103 Norm. (1.84%)
σ3He/σD
1.1
1
0.9
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
FIG. 3 (color online). EMC ratio for 3 He [17]. The upper
squares are the raw 3 He=2 H ratios, while the bottom circles
show the isoscalar EMC ratio (see text). The triangles are the
HERMES results [10] which use a different isoscalar correction.
The solid (dashed) curves are the SLAC A-dependent fits to
carbon and 3 He.
Ref. [13] to yield the neutron-to-proton cross section ratio
in nuclei. Using the ‘‘smeared’’ proton and neutron cross
section ratios more accurately reflects the correction that
should be applied to the nuclear ratios, and in the end,
yields a significantly smaller correction at large x, where
the uncertainty in the neutron structure function is largest.
While applying the isoscalar correction to the 3 He data
using the smeared F2n =F2p ratio yields a more reliable
result, there is still some model dependence to this correction due to the uncertainty in our knowledge of the neutron
structure function. Ref. [13] demonstrated that much of the
inconsistency between different extractions of the neutron
structure function comes from comparing fixed-Q2 calculation to data with varying Q2 values, rather than from the
underlying assumptions of nuclear effects in the deuteron.
Nuclear effects beyond what is included in Ref. [13], such
as the off-shell contribution ðoffÞ of Ref. [14], yield a 1%–
2% decrease to the proton’s contribution to the deuteron
thus increasing the extracted F2n =F2p ratio by 0.01–0.02.
This yields a slightly reduced correction for 3 He which
would raise the isoscalar EMC ratio for 3 He by 0.3%–0.6%
at our kinematics.
The observed nuclear effects are clearly smaller for 3 He
than for 4 He and 12 C. This is again consistent with models
where the EMC effect scales with the average density, as
the average density for 3 He is roughly half that of the 12 C.
However, the results of 9 Be are not consistent with the
simple density-dependent fits. The observed EMC effect in
3
He is essentially identical to what is seen in 12 C, even
though the density of 9 Be is much lower. This suggests that
both the simple mass- or density-scaling models break
down for light nuclei.
One can examine the nuclear dependence based on the
size of the EMC ratio at a fixed x value, but the normal-
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ization uncertainties become a significant limiting factor. If
we assume that the shape of the EMC effect is universal,
and only the magnitude varies with target nucleus, we can
compare light nuclei by taking the x dependence of the
ratio in the linear region, 0:35 < x < 0:7, using the slope as
a measure of the relative size of the EMC effect that is
largely unaffected by the normalization. The slopes are
shown for light nuclei in Fig. 4 as a function of average
nuclear density. The average density is calculated from the
ab initio Greens Function Monte Carlo calculation of the
spatial distributions [15]. Because we expect that it is the
presence of the other (A 1) nucleons that yields the
modification to the nuclear structure function, we choose
to scale down this density by a factor of ðA 1Þ=A, to
remove the struck nucleon’s contribution to the average
density. The EMC effect for 3 He is roughly one third of the
effect in 4 He, in contrast to the A-dependent fit to the SLAC
data [2], while the large EMC effect in 9 Be contradicts a
simple density-dependent effect.
One explanation for the anomalous behavior of 9 Be is
that it can be described as a pair of tightly bound alpha
particles plus one additional neutron [16]. While most of
the nucleons are in a dense environment, similar to 4 He, the
average density is much lower, as the alphas (and additional neutron) ‘‘orbit’’ in a larger volume. This suggests
that it is the local density that drives the modification. The
strong clustering of nucleons in 9 Be leads to a special case
where the average density does not reflect the local environment of the bulk of the protons and neutrons.
Another possibility is that the x dependence of the EMC
effect is different enough in these light nuclei that we
cannot use the falloff with x as an exact measure of the
relative size of the EMC effect. This too suggests that the
EMC effect is sensitive to the details of the nuclear structure, which would require further theoretical examination.
At the moment, there are almost no calculations for light
nuclei that include detailed nuclear structure.
FIG. 4 (color online). The circles show the slope of the isoscalar EMC ratio for 0:35 < x < 0:7 as a function of nuclear
density. Error bars include statistical and systematic uncertainties.
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In conclusion, we have measured the nuclear dependence of the structure functions for a series of light nuclei.
This data set provides significantly improved data on 4 He
and the first valence-region measurement on 3 He, as well
as extending the measurements to higher x for other light
nuclei. This will allow for more detailed comparison with
calculations that include binding and Fermi motion, providing a more reliable baseline at low x, where these
effects are still important, but may not fully explain the
observed nuclear dependence.
These data also provide model independent information
on the scaling of the nuclear effects. Under the assumption
that the shape of the EMC effect is the same for all nuclei,
the large difference between 3 He and 4 He rules out previous A-dependent fits, while the EMC effect in 9 Be is
inconsistent with models where the effect scales with
average density. The results are consistent with the idea
that the effect scales with the local environment of the
nucleons, or require that the x dependence of the effect
changes in very light nuclei.
This work was supported in part by the NSF and DOE,
including DOE Contract No. DE-AC02-06CH11357, DOE
Contract No. DE-AC05-06OR23177 under which JSA,
LLC operates JLab, and the South African National
Research Foundation.
‡
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
*Corresponding author: johna@anl.gov
†
Deceased
202301-5
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Present
address:
University
of
Johannesburg,
Johannesburg, South Africa.
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See EPAPS Document No. E-PRLTAO-103-015948 for
data tables and figures. They are also available for download at http://hallcweb.jlab.org/experiments/E03103. For
more information on EPAPS, see http://www.aip.org/
pubservs/epaps.html.